Question

求高数大神解答。

求高数大神解答。这一部怎么来的。

Answer 1

∫(0->π/2) dθ = π/2
∫(0->π/2) dθ .∫(0->1) (1-r^2)/(1+r^2) dr
=(π/2)∫(0->1) (1-r^2)/(1+r^2) dr
=(π/2)∫(0->1) [-(1+r^2) + 2 ]/(1+r^2) dr
=(π/2)∫(0->1) [-1 + 2/(1+r^2)] dr
=(π/2)[-r + 2arctanr]|(0->1)
=(π/2)(-1 + π/2)